Arianna and her children went into a restaurant and she bought $44 worth of hamburgers and drinks. Each hamburger costs $5.50 and each drink costs $2.75. She bought 4 more drinks than hamburgers. Graphically solve a system of equations in order to determine the number of hamburgers, x, commax, and the number of drinks, y, commay, that Arianna bought.

Question

Arianna and her children went into a restaurant and she bought $44 worth of hamburgers and drinks. Each hamburger costs $5.50 and each drink costs $2.75. She bought 4 more drinks than hamburgers. Graphically solve a system of equations in order to determine the number of hamburgers, x, commax, and the number of drinks, y, commay, that Arianna bought.

Answer 1

Let x be the number of hamburgers and y be the number of drinks that Arianna bought.

According to the problem, the total cost of hamburgers and drinks is $44.
So the equation is:
5.50x + 2.75y = 44
The problem also states that Arianna bought 4 more drinks than hamburgers.
So, the equation is:
y = x + 4
To solve this system of equations, we can graphically represent them using the x and y-axis.
At x = 0, y = 0 + 4 = 4
At y = 0, x = 0
Plotting these points on the graph, we get:
{{Graph1 |xLeft =-50|xRight=50|yTop = 20|yBottom = -10|xLabel =x|yLabel=y|Ignore Line = true}}

The intersection point of the two lines is (6, 10).
Therefore, she bought 6 hamburgers and 10 drinks.